GAMMA - Maple Help

convert/GAMMA

convert factorials and binomials to GAMMAs

Calling Sequence

 convert(expr, GAMMA, indets) $\mathrm{convert}\left(\mathrm{expr},\mathrm{\Gamma },\mathrm{indets}\right)$

Parameters

 expr - expression indets - (optional) indeterminate or set of indeterminates

Description

 • The convert/GAMMA function converts factorials, binomials and multinomial coefficients in an expression to the GAMMA function.
 • You can enter the command convert/GAMMA using either the 1-D or 2-D calling sequence. For example, convert(x!, GAMMA) is equivalent to $\mathrm{convert}\left(x!,\mathrm{\Gamma }\right)$.
 • If an indeterminate or set of indeterminates is specified, then only factorials and binomials involving a specified indeterminate will be converted to the GAMMA function.

Examples

 > $\mathrm{convert}\left(x!,\mathrm{\Gamma }\right)$
 ${\mathrm{\Gamma }}{}\left({x}{+}{1}\right)$ (1)
 > $\mathrm{convert}\left(\mathrm{binomial}\left(m,3\right),\mathrm{\Gamma }\right)$
 $\frac{{\mathrm{\Gamma }}{}\left({m}{+}{1}\right)}{{6}{}{\mathrm{\Gamma }}{}\left({m}{-}{2}\right)}$ (2)
 > $\mathrm{convert}\left(x!y!z!,\mathrm{\Gamma },\left\{x,y\right\}\right)$
 ${\mathrm{\Gamma }}{}\left({x}{+}{1}\right){}{\mathrm{\Gamma }}{}\left({y}{+}{1}\right){}{z}{!}$ (3)
 > $\mathrm{convert}\left(\left(x+y\right)!,\mathrm{\Gamma },\left\{x,y\right\}\right)$
 ${\mathrm{\Gamma }}{}\left({x}{+}{y}{+}{1}\right)$ (4)